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Answer :
To analyze the work used to write an equivalent equation for [tex]\( y \)[/tex] in the equation [tex]\( 3y = 36 - 5x \)[/tex], let's walk through the process step-by-step:
1. Divide both sides by 3:
- The goal here is to isolate [tex]\( y \)[/tex] on one side of the equation.
- Start by dividing the entire left side and each term on the right side by 3.
2. Simplify the left side:
- [tex]\( \frac{3y}{3} = y \)[/tex]
3. Simplify the right side:
- First Term: [tex]\( \frac{36}{3} = 12 \)[/tex]
- Second Term: [tex]\( \frac{-5x}{3} = -\frac{5}{3}x \)[/tex]
4. Rewrite the equation:
- After dividing each term on the right side by 3, the equation becomes:
- [tex]\( y = 12 - \frac{5}{3}x \)[/tex]
Conclusion:
- The original division was performed incorrectly in the given work. Both terms on the right side of the equation need to be individually divided by 3, in particular the second term, which involves [tex]\( x \)[/tex].
- The correct equation, after performing these operations, is [tex]\( y = 12 - \frac{5}{3}x \)[/tex].
This process shows that the given solution originally did not properly divide the [tex]\( -5x \)[/tex] term by 3, leading to an incorrect conclusion in the initial work.
1. Divide both sides by 3:
- The goal here is to isolate [tex]\( y \)[/tex] on one side of the equation.
- Start by dividing the entire left side and each term on the right side by 3.
2. Simplify the left side:
- [tex]\( \frac{3y}{3} = y \)[/tex]
3. Simplify the right side:
- First Term: [tex]\( \frac{36}{3} = 12 \)[/tex]
- Second Term: [tex]\( \frac{-5x}{3} = -\frac{5}{3}x \)[/tex]
4. Rewrite the equation:
- After dividing each term on the right side by 3, the equation becomes:
- [tex]\( y = 12 - \frac{5}{3}x \)[/tex]
Conclusion:
- The original division was performed incorrectly in the given work. Both terms on the right side of the equation need to be individually divided by 3, in particular the second term, which involves [tex]\( x \)[/tex].
- The correct equation, after performing these operations, is [tex]\( y = 12 - \frac{5}{3}x \)[/tex].
This process shows that the given solution originally did not properly divide the [tex]\( -5x \)[/tex] term by 3, leading to an incorrect conclusion in the initial work.
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